Laser-phase determination methods and transfer equations for direct temporal structure measure- ments of atto- and femtosecond XUV pulses

In this paper the laser-phase determination methods and transfer equations are presented to directly reconstruct the detailed temporal structures of ultra-short extreme ultraviolet (xuv) pulses from the measured photoelectron energy spectra (PES). Each transfer equation includes one of PID (proportional-integral-differential) terms of PES. The intensity and instantaneous frequency of attosecond xuv can be retrieved from the integral term of PES. The intensity profiles of narrow bandwidth atto- and femtosecond xuvs can be rebuilt from the proportional and differential terms of PES respectively. The methods and equations may be used to improve time resolutions in measuring ultrashort pulses.